Positron emission tomography

Positron emission tomography (PET) is a modality to generate images, mostly of internal organs, via the use of a radiotracer, which is a labelled radioactive isotope. A typical example is fluorodeoxyglucose and abbreviated , \[^{18}\\]F-FDG or FDG used in the medical imaging. In the target organ, a nuclear process occurs, and a positron is emitted. Within a short-range, this particle is captured by an electron, a process known as annihilation. Two photons are released, and they travel in a straight line opposite to each other. Arrays of detectors commonly arranged in a circular fashion detect the photons, in coincidence. An electrical signal recorded in the form of and event. In our DAQ system, and the event is recorded in a binary file after a trigger. In this repository are programs in C++, Python, OpenCV, Jave (Imagej) to perform

• Conversion from binary to text and castor CDF format.
• Processing of normalization data used for image correction
• Image reconstruction using Maximum Likelihood implemented in castor-recon., C++ base
• Visualization of data
• NEMA standards implemented in Imagej

1. Data file

The event constitutes 4 segments

1. Detector event recoded as 1, 0., for example, 1100 means detector 1 and 2 fired and detector 3 and 4 were off, of 1111 means all four detectors fires.
2. The next event is conditional on the number of detectors that fired. If detector event is 1100 as above, x1, y1, e1, and x2, y2, e2 are measured. These are correspondingly the x location, y location, and energy.
3. The time is the last thing to record.

2. Data conversion

castor-recon accepts a specific format of data called CDF. Details description is on the wbsite. Provided in the program folder is a C++ program that converts binary to CDF. PET images suffer from various errors that must be corrected. We have data for normalization correction and will be processed in the appropriate format. There are two CDF formats,

1. Listmode: the events are recorded as a list. Every event that comes in the append to the file. The program to convert binary to bin file is in foleder[todo]
2. Histogram mode: In the histogram mode, the data are bin to each LOR. The radioactive decay correction is applied as the events are binned. The file is located in [todo]

3. Normalization correction

Here, we will deal with normalization errors. These are errors that arise due to the inherent geometry of the system. A simple way to think of it is that if a cylindrical source is used, the density of lines through the center will be higher than at the edge, creating a fictitious high density at the center. To correct this, we use a flat phantom and place it with it face adjacent to the detectors. Events recorded are then processed. One technique used to improve the statistics is called fan-sum which helps reduce the variance. A sketch is shown below of the process used to variance reduction. .

In a simples way, the main assumption is that the phantom has a uniform variation in intensity. So, the coouts in detector $i$ in coincidence with a group of detectors B is improved by summing all the counts in B. By summing the count in the group, the statistics is improved without any information leakage.

4. Scattering Correction

Scatter events are inevitaible in PET systems. There are some techniques developed to measure scattering data by using CT. Here we design a method to use the energy distribution per LOR to estimate the scatter correction. These are inturn fed into the image reconstruction algorithm. This leads to a two way process.

5. Data visualization

Several data visualizations files are in the repo. Images and normalization coefficients visualized. Outlier detection methods are applied to identify dead pixels.

5. NEMA standards implemented in ImageJ

NEMA - NU 2004 standards are a set of rules defined to facilitate the comparison of results across different systems.